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gsortsh

Sort a strided array using Shellsort.

Installation

npm install @stdlib/blas-ext-base-gsortsh

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var gsortsh = require( '@stdlib/blas-ext-base-gsortsh' );

gsortsh( N, order, x, stride )

Sorts a strided array x using Shellsort.

var x = [ 1.0, -2.0, 3.0, -4.0 ];

gsortsh( x.length, 1.0, x, 1 );
// x => [ -4.0, -2.0, 1.0, 3.0 ]

The function has the following parameters:

• N: number of indexed elements.
• order: sort order. If order < 0.0, the input strided array is sorted in decreasing order. If order > 0.0, the input strided array is sorted in increasing order. If order == 0.0, the input strided array is left unchanged.
• x: input Array or typed array.
• stride: index increment.

The N and stride parameters determine which elements in x are accessed at runtime. For example, to sort every other element

var floor = require( '@stdlib/math-base-special-floor' );

var x = [ 1.0, -2.0, 3.0, -4.0 ];
var N = floor( x.length / 2 );

gsortsh( N, -1.0, x, 2 );
// x => [ 3.0, -2.0, 1.0, -4.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

// Initial array...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );

// Create an offset view...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length/2 );

// Sort every other element...
gsortsh( N, -1.0, x1, 2 );
// x0 => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ]

gsortsh.ndarray( N, order, x, stride, offset )

Sorts a strided array x using Shellsort and alternative indexing semantics.

var x = [ 1.0, -2.0, 3.0, -4.0 ];

gsortsh.ndarray( x.length, 1.0, x, 1, 0 );
// x => [ -4.0, -2.0, 1.0, 3.0 ]

The function has the following additional parameters:

• offset: starting index.

While typed array views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to access only the last three elements of x

var x = [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ];

gsortsh.ndarray( 3, 1.0, x, 1, x.length-3 );
// x => [ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]

Notes

• If N <= 0 or order == 0.0, both functions return x unchanged.
• The algorithm distinguishes between -0 and +0. When sorted in increasing order, -0 is sorted before +0. When sorted in decreasing order, -0 is sorted after +0.
• The algorithm sorts NaN values to the end. When sorted in increasing order, NaN values are sorted last. When sorted in decreasing order, NaN values are sorted first.
• The algorithm has space complexity O(1) and worst case time complexity O(N^(4/3)).
• The algorithm is efficient for shorter strided arrays (typically N <= 50).
• The algorithm is unstable, meaning that the algorithm may change the order of strided array elements which are equal or equivalent (e.g., NaN values).
• The input strided array is sorted in-place (i.e., the input strided array is mutated).
• Depending on the environment, the typed versions (dsortsh, ssortsh, etc.) are likely to be significantly more performant.

Examples

var round = require( '@stdlib/math-base-special-round' );
var randu = require( '@stdlib/random-base-randu' );
var Float64Array = require( '@stdlib/array-float64' );
var gsortsh = require( '@stdlib/blas-ext-base-gsortsh' );

var rand;
var sign;
var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    rand = round( randu()*100.0 );
    sign = randu();
    if ( sign < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    x[ i ] = sign * rand;
}
console.log( x );

gsortsh( x.length, -1.0, x, -1 );
console.log( x );

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References

• Shell, Donald L. 1959. "A High-Speed Sorting Procedure." Communications of the ACM 2 (7). Association for Computing Machinery: 30–32. doi:10.1145/368370.368387.
• Sedgewick, Robert. 1986. "A new upper bound for Shellsort." Journal of Algorithms 7 (2): 159–73. doi:10.1016/0196-6774(86)90001-5.
• Ciura, Marcin. 2001. "Best Increments for the Average Case of Shellsort." In Fundamentals of Computation Theory, 106–17. Springer Berlin Heidelberg. doi:10.1007/3-540-44669-9_12.

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See Also

• @stdlib/blas-ext/base/dsortsh: sort a double-precision floating-point strided array using Shellsort.
• @stdlib/blas-ext/base/gsort2sh: simultaneously sort two strided arrays based on the sort order of the first array using Shellsort.
• @stdlib/blas-ext/base/ssortsh: sort a single-precision floating-point strided array using Shellsort.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

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